Research
Research
Research
Research
2,844+ open-access research outputs.
Large language models (LLMs) conventionally process structured inputs as 1D token sequences. While natural for prose, such linearization may introduce additional representational burden for tasks whos…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Att…
In this paper we consider higher order Schr\"odinger operators $$\mathcal L u=Lu+Vu,$$ where $L$ denotes a fourth order operator and $V\geq 0$ a suitable potential. We initiate our analysis by conside…
The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successf…
We establish the existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory. Notably, the existence of a positive-curvature Einstein …
We introduce and study the finite-approximate solvability of operator equations \(Lu = h\) in a Hilbert space setting, where a bounded operator \(L \colon U \to H\) is paired with a finite-dimensional…
Traditional step-stress accelerated life testing models assume that the test units originate from a homogeneous population. Recently, Lu and Kateri (2025) proposed a heterogeneous cumulative exposure …
Correlations between the localized and conductive spins/charges have been the central issue of various fascinating quantum phenomena found on itinerant electron systems. Here, the obvious multiplet st…
Phase-field models for anisotropic fracture employ two complementary mechanisms: (i) the anisotropic crack density function, controlling direction-dependent fracture resistance, and (ii) the anisotrop…
Using density functional theory, we study the influence of hydrostatic pressure on the crystal structure of lanthanide monoxides, focusing on the monoxides formed by the fifteen elements of the lantha…
A central theme in extremal combinatorics is the study of the maximum number of edges in an $r$-uniform hypergraph ($r$-graph) with matching number at most $s$ (the Erd\H{o}s Matching Conjecture) or w…
In this study, surface-enhanced Raman scattering (SERS) and density functional theory (DFT) calculations were combined to investigate the SERS spectra of Ln-citrate complexes (Ln: Tb, Dy, Ho, Er, Tm, …
We propose a novel entropy flow on weighted graphs, which provides a principled framework that characterizes the evolution of probability distributions over graph structures while sharing geometric in…
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testi…
We prove an explicit finite-sample version of the Borel--Cantelli lemma under $m$-dependence. Given any $m$-dependent sequence of events $(A_k)_{1\leq k\leq N}$, we show that \[ \mathbb{P}\Bigl(\big…
Autoregressive graph generators define likelihoods via a sequential construction process, but these likelihoods are only meaningful if they are consistent across all linearizations of the same graph. …
This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserstein Distance and optimal transport theory. We present some o…
We study the three-dimensional incompressible Navier-Stokes system on $\mathbb{R}^3$ with an additional dissipative nonlocal term \[ \partial_t u + (u\cdot\nabla)u + \nabla p = \nu \Delta u + Lu, \qqu…
This study aimed to analyze the time series behavior of the Southern Oscillation Index through techniques using Fast Fourier Transform, computing the autocorrelation function, and the calculation of t…
In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this cur…
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